Hello  

Following are the few government departments, where you can seek current openings for computer engineers.

• Center for Development of Advance Computing (CDAC): 
• Steel Authority of India (SAIL): 
• Coal India Limited (CIL):
• Defence Research & Development Organisation (DRDO):
• Electronics Corporation of India Limited (ECIL
• Bharat Petroleum Corporation Limited (BPCL)
• Bharat Electronics Limited (BEL)
• Central Bureau of Investigation (CBI)
• Intelligence Bureau (IB)
• Heavy Engineering Corporation Ltd. (HEC)
• Indian Space Research Organization (ISRO)
• Indian Oil Corporation Ltd. (IOCL)

Hope this helped. 

Good luck!